Can Dispersive Pressure Cause Inverse Grading in Grain Flows?: Reply

Dispersions of solid spherical grains of diameter D = 0.13cm were sheared in Newtonian fluids of varying viscosity (water and a glycerine-water-alcohol mixture) in the annular space between two concentric drums. The density σ of the grains was balanced against the density ρ of the fluid, giving a condition of no differential forces due to radial acceleration. The volume concentration C of the grains was varied between 62 and 13 %. A substantial radial dispersive pressure was found to be exerted between the grains. This was measured as an increase of static pressure in the inner stationary drum which had a deformable periphery. The torque on the inner drum was also measured. The dispersive pressure P was found to be proportional to a shear stress λ attributable to the presence of the grains. The linear grain concentration λ is defined as the ratio grain diameter/mean free dispersion distance and is related to C by λ = 1 ( C 0 / C ) 1 2 − 1 where C 0 is the maximum possible static volume concentration. Both the stresses T and P , as dimensionless groups T σ D 2 /λη 2 , and P σ D 2 /λη 2 , were found to bear single-valued empirical relations to a dimensionless shear strain group λ ½ σ D 2 (d U /d y )lη for all the values of λ< 12( C = 57% approx.) where d U /d y is the rate of shearing of the grains over one another, and η the fluid viscosity. This relation gives T α σ ( λ D ) 2 ( dU / dy ) 2 and T ∝ λ 1 2 η d U / dy according as d U /d y is large or small, i.e. according to whether grain inertia or fluid viscosity dominate. An alternative semi-empirical relation F = (1+λ)(1+½λ)ηd U /d y was found for the viscous case, when T is the whole shear stress. The ratio T/P was constant at 0·3 approx, in the inertia region, and at 0.75 approx, in the viscous region. The results are applied to a few hitherto unexplained natural phenomena.

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Dispersive Pressure, Boundary Jerk and Configurational Changes in Debris Flows

International Journal of Erosion Control Engineering ◽

10.13101/ijece.9.1 ◽

2016 ◽

Vol 9 (1) ◽

pp. 1-6 ◽

Cited By ~ 1

Author(s):

Perry BARTELT ◽

Brian McARDELL ◽

Christoph GRAF ◽

Marc CHRISTEN ◽

Othmar BUSER

Keyword(s):

Debris Flows ◽

Dispersive Pressure

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Dispersive pressure and density variations in snow avalanches

Journal of Glaciology ◽

10.3189/002214311798043870 ◽

2011 ◽

Vol 57 (205) ◽

pp. 857-860 ◽

Cited By ~ 12

Author(s):

Othmar Buser ◽

Perry Bartelt

Keyword(s):

Kinetic Energy ◽

Mechanical Energy ◽

Center Of Mass ◽

Random Fluctuation ◽

Flow Density ◽

Snow Avalanches ◽

Mean Velocity ◽

The Mean ◽

Dispersive Pressure ◽

Fluctuation Energy

AbstractSnow avalanches possess two types of kinetic energy: the kinetic energy associated with the mean velocity in the downhill direction and the kinetic energy associated with individual particle velocities that vary from the mean. The mean kinetic energy is directional; the kinetic energy associated with the velocity fluctuations is non-directional in the sense that it is connected to random particle movements. However, the rigid, basal boundary directs the random fluctuation energy into the avalanche. Thus, the random energy flux is converted to free mechanical energy which lifts and dilates the avalanche flow mass, changing the flow density and increasing the normal (dispersive) pressure and, as a consequence, changing the flow resistance. In this paper we derive macroscopic relations that link the production of the random kinetic energy to the perpendicular acceleration of the avalanche’s center of mass. We show that a single burst of fluctuation energy will produce pressures that oscillate around the hydrostatic pressure. Because we do not include a damping process, the oscillations of the center of mass remain, even if the production of random kinetic energy stops. We formulate relationships that can be used within the framework of depth-averaged mass and momentum equations that are often used to simulate snow avalanches in realistic terrain.

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Discussion of “The relation between dilatancy, effective stress and dispersive pressure in granular avalanches” by P. Bartelt and O. Buser (DOI: 10.1007/s11440-016-0463-7)

Acta Geotechnica ◽

10.1007/s11440-016-0502-4 ◽

2016 ◽

Vol 11 (6) ◽

pp. 1465-1468

Author(s):

Richard M. Iverson ◽

David L. George

Keyword(s):

Effective Stress ◽

Dispersive Pressure

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An energy-based method to calculate streamwise density variations in snow avalanches

Journal of Glaciology ◽

10.3189/2015jog14j054 ◽

2015 ◽

Vol 61 (227) ◽

pp. 563-575 ◽

Cited By ~ 11

Author(s):

Othmar Buser ◽

Perry Bartelt

Keyword(s):

Mechanical Energy ◽

Center Of Mass ◽

Flow Regimes ◽

Basic Feature ◽

Flow Density ◽

Snow Avalanches ◽

Velocity Fluctuations ◽

Gravity Driven ◽

The Mean ◽

Dispersive Pressure

AbstractSnow avalanches are gravity-driven flows consisting of hard snow/ice particles. Depending on the snow quality, particularly temperature, avalanches exhibit different flow regimes, varying from dense flowing avalanches to highly disperse, mixed flowing-powder avalanches. In this paper we investigate how particle interactions lead to streamwise density variations, and therefore an understanding of why avalanches exhibit different flow types. A basic feature of our model is to distinguish between the velocity of the avalanche in the mean, downslope direction and the velocity fluctuations around the mean, associated with random particle movements. The mechanical energy associated with the velocity fluctuations is not entirely kinetic, as particle movements in the slope-perpendicular direction are inhibited by the hard boundary at the bottom giving rise to a change in flow height and therefore change in flow density. However, this volume expansion cannot occur without raising the center of mass of the particle ensemble, i.e. an acceleration, which, in turn, exerts a pressure on the bottom, the so-called dispersive pressure. As soon as the volume no longer expands, the dispersive pressure vanishes and the pressure returns to the hydrostatic pressure. Different streamwise density distributions, and therefore different avalanche flow regimes, are possible.

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